String Cosmology: A Brief Overview

Bin Chen

Dep. of Phys., Peking Univ.

28th. June, 2008

Questions with cosmology SM:

What happens at a cosmological singularity?Does time begin?What is the quantum vacuum for gravitational fields?Is there a future asym. vacuum state?Why are there three large spatial coor.?What is dark energy?What is dark matter?……

Need a quantum theory of gravity!

What is string/M theory?

A theory of quantum gravity. The most promising candidate to unify all the elementary particles and forces in nature including gravity.

Elementary particles: strings at Planckian scale. All usual particles emerge as the excitations of the string.

Einstein’s dream: all the forces and particles emerge in an elegant geometrical way;

Incredible rich structure; Achievements: blackhole entropy, AdS/CFT correspondence, new ideas;

Challenges:What is string theory? its basic principle,its structure, SFT,nonperturbative description,…

Experimental evidence? Lab. experiment impossible; very early universe is the best and only lab.;

......

String Cosmology

Intersection between string/M and cosmology: cosmology can be the key to the verification of string theory, and string theory can be what we need to solve some deep puzzles in cosmology.

Topics: (String cosmology 2003, KITP)

Nature of the Big bang singularity;Models of inflation based on string theory moduli;Cosmology from Big crunch to Big bang;Cosmology and holographic principle;Quantum theory of Asym. de Sitter univ.Possible imprints of string physics on observational cosmology;……Landscape;

1. Cosmological Singularity

In principle, there is no singularity in string theory due to the existence of the minimal string scale;In GR, the singularity in terms of geodesic incompleteness; (in the sense of point particle)

In string theory, strings see the spacetime only through the sigma model;

Spacetime in string theoryNonconventional;(string as probe)

The fuzziness of the event; Stringy geometry: the singularities (orbifolds, conifold) resolved; mirror symmetry, topology transition …; Quantum foam; Emergent spacetime; (nonperturbative)

Remarks:T-duality: R~1/R;Resolution of the singularities: new degrees of freedom; Static singularities: orbifold and conifold;

Time-dependent singularities?Provide the initial state;

Difficulties: (perturbatively) Short of workable models;Trouble with the vacuum; (same as QFTs in the curved spacetime)

Large backreaction;Perturbation theory could break down;

Suggestions:

String theory in the time-dependent backgrounds; (Rolling tachyon, Null orbifolds, …)

Nonperturbative string theory;(Matrix model, SFT, Matrix cosmology,…)

Blackhole singularities; (AdS/CFT, …)

Holographic principle; (Holographic cosmology, …)

New idea or concept to have a better understanding of the string theory !

Emergent spacetimeAdS/CFT correspondence: gravity in 5-dim Anti-de-Sitter spacetime is equivalent to a 4-dim. gauge theory; (J. Maldacena, …)

Lesson: the usual concept of spacetime in terms of metric could be broken down near cosmological singularity;

Is time emergent? Space being emergent has been shown in many examples; no concrete example for emergent time;

2. Inflation or something else

How we get inflation in string theory? From compactification 10D4D, there are large number of moduli (scalars): very flat potential and moduli fixing; (KKLMMT model, …)

Brane world; (Dvali, H. Tye, et.al….)

warp geometry: TeV string scale; DBI inflation: large non-Gaussianity and tensor

mode, cosmic string production,……;

Alternative to inflation: Ekpyrotic models; (P. J. Steinhardt, et.al.)

String cosmology ( in a specific sense): Pre-Big-bang scenario; (G. Veneziano et.al.)

String gas model; (R. Brandenberger, et.al.)……

3. Stringy signature:

Transplanckian physics: Ripple at sub-Planckian could leave imprint; (Brandenberger, Starobinsky, …)

modified dispersion relation, noncommutative inflation, alpha-vacuum, ……

Cosmic superstrings: produced after inflation; (Polchinski, Dvali, … 2003)

different from cosmic string in QFT

Extra dimensions; (RS, …)

Particular signatures from brane inflation;

Conclusion

Modern cosmology is becoming an exact science with a fruitful and rapid intersection between observation and theory;Fundamental issues require a quantum theory of gravity;String cosmology is promising!Challenges to string theory;

Thank you